## Course Summary

When a person thinks of algebra, they typically think of a process used to solve polynomial equations. Modern algebra, the subject of Math 305, is a discipline developed to answer precisely when formulas for solving equations exist. We all know the quadratic formula for solving degree $2$ polynomial equations, and there are even cubic and quartic equations as well. One of the most surprising theorems in algebra was discovered in the early 1800s when it was proven that the general quintic equation has roots which cannot be expressed using addition, subtraction, multiplication, division and root extraction for rational numbers; somehow these polynomials are too complex to allow for a ``quintic formula."

The machinery necessary to understand this result includes several classes of mathematical objects which are abstractions of some familiar mathematical friends (most notably, the collection of integers, which is often written $\mathbb{Z}$). This class will be your introduction to these basic objects. We will spend the majority of our class time discussing *groups*, which is a set of elements which can be combined under a binary operation. Closer to the end of the semester we'll also consider algebraic sets which have even more structure than groups. Throughout the semester we will occasionally discuss how ideas from modern algebra appear in in everyday life, though most of our time together will be spent fully embracing the abstract nature of the discipline.

## Course Instructor

The professor for this class is Andy Schultz. His office is on the third floor of the Science Center, room S352. His office hours are Monday from 3-4, Tuesday from 2:45-3:45, Wednesday from 9-10, Thursday from 10-11 and Friday from 9:30 to 10:30. You are highly encouraged to attend office hours, and you never need an appointment to do so. If these office hours don't fit with your schedule, contact the instructor so that he can either adjust when ``official" office hours are held or set up an appointment to help you outside of office hours.

You can contact the instructor at . Though he is always happy to receive emails from you with questions or concerns about the course, he can't guarantee that he'll be able to promptly reply to emails late at night or over the weekend. If you do contact the professor by email, please be sure to follow standard email etiquette. In particular, please make sure you include a greeting and signature and avoid abbreviations. If you're contacting him to ask about a problem, please be sure to specify what the problem asks (as opposed to asking something like ``I can't get problem 2 and need your help").